I need some Math Help
I'm doing some worksheets on Trigonometry.
Here are the 5 questions I'm stuck on.
Help is appreciated <3 Preferably step by step.
1. Sin(-Pi/6) + cos(7pi/4) Find exact values. (EDIT: SOLVED)
2. (-5/13, 12/13) Find 6 trig ratios, exact. (EDIT: SOLVED)
3. Csc= -8/5 Pi<Theta<3Pi/2 Find TanTheta. (SOLVED)
4.Tan=5/2 0<Theta<2Pi Find longest positive value, in Radians.
5. A= (Root 3 over 2, 1/2)
B= (- Root 2 over 2, Root 2 over 2)
A and B can be found using the formula aPi/b
Find A & B.
0<Theta<Pi.
October 10, 2012
6 Comments • Newest first
Ugh.... Number 5...
@InSovietRussia: Yup
H=8
A=5
O=x
X^2 + A^2 = H^2
X^2 + 25 = 64
X^2 = 39
X=+-sqrt(39)
[quote=LikedBandit]number 3 is sqrt(39)/5.
1/cos(theta) = -8/5
cos(theta) = -5/8
draw a triangle, find that the opposite side = +-sqrt(39)
tan(theta) = o/a = +-sqrt(39)/5 but because tan is positive in quadrant 3, tan(theta) = sqrt(39)/5[/quote]
I'm a little bit confused on the Draw Triangle to find Opposite side.
Do I use Pythagoras?
number 3 is sqrt(39)/5.
1/cos(theta) = -8/5
cos(theta) = -5/8
draw a triangle, find that the opposite side = +-sqrt(39)
tan(theta) = o/a = +-sqrt(39)/5 but because tan is positive in quadrant 3, tan(theta) = sqrt(39)/5
Thank you.
Any insights on numbers 3~5?
For number 1 you are given your angle in radians. Have you learned the unit circle yet? Convert radians into degrees. -Pi/6 = -30 Degrees, 7Pi/4 = 315 degrees. So it's like doing Sin-30degrees + cos315degrees. Find your reference angles, which would be 30 and 45. Find Sin30 and Cos45, since in the original problem you had -30, it's in the 4th quadrant and sin will always be negative there. Cos315 also lies withing the fourth quadrant, but cos is always positive in the fourth quadrant so the answer remains positive. Your problem should look like this, -1/x^1/2 +1/x^1/2 (x^1/2 is the same thing as squareroot of x). Usually when you have a square root in the denominator you would have to rationalize them but this seems to add up to zero anyway so it doesn't matter here.
For number 2, you are given a coordinate. Cos corresponds to your x-value and sin corresponds to your y-value. So instead of (x,y) you have (cos,sin). So right there you already have two of the trig ratios. From there you know that tan=sin/cos, cot=cos/sin, Secant=1/cos, cosecant=1/sin